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Guided Wave Propagation in Functionally Graded One-Dimensional Hexagonal Quasi-Crystal Plates

Published online by Cambridge University Press:  14 October 2020

B. Zhang ,
J.G. Yu Open the ORCID record for J.G. Yu [Opens in a new window]  and
X.M. Zhang
B. Zhang
Affiliation:
School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo, China
J.G. Yu*
Affiliation:
School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo, China
X.M. Zhang
Affiliation:
School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo, China
*
*Corresponding author ([email protected])
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Abstract

Due to the high brittleness, cracks, holes, and other defects that are easily generated in quasi-crystal structures can affect safe applications in serious cases. For guided wave non-destructive testing, the propagation of Lamb and SH waves in functionally graded one-dimensional hexagonal quasi-crystal plates are investigated. Governing equations of wave motion in the context of Bak’s model are deduced and solved by the Legendre orthogonal polynomial method. Dispersion curves, phonon and phason displacement, and stress distributions are illustrated. The convergence of the present method applied to functionally graded quasi-crystal plates is verified. Moreover, the influences of the phonon-phason coupling effect and graded fields on wave characteristics are analyzed. Some new results are obtained: angular frequencies of phason modes always decrease as phonon-phason coupling coefficients, Ri, increase; and phonon and phason displacements of Lamb and SH waves at high frequencies are mainly distributed in the region that contains more quasi-crystal material with a smaller elasticity modulus and less rigidity. The obtained results establish the theoretical foundation of guided wave non-destructive testing for functionally graded quasi-crystal plates.

Keywords

Functionally graded materialQuasi-crystalPhonon-phason coupling effectGuided wave
Type
Research Article
Information
Journal of Mechanics , Volume 36 , Issue 6 , December 2020 , pp. 773 - 788
Copyright
Copyright © 2020 The Society of Theoretical and Applied Mechanics

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References

REFERENCES

Shechtman, D.G., Blech, I.A., Gratias, D., and Cahn, J.W., “Metalic Phase with Long-Range Orientational Order and No Translational Symmetry,” Physical Review Letters, 53(20), pp.1951-1953, (1984).CrossRefGoogle Scholar
Fan, T.Y., “Development on Mathematical Theory of Elasticity of Quasicrystals and Some Relevant Topics,” Advances in Mechanics, 42(5), pp.501-521, (2012).Google Scholar
Qian, C. and Wang, J.G., “Progress in Quasicrystals and Their Properties Research,” Journal of Harbin institute of technology, 49(7), pp.1-11, (2017).Google Scholar
Kenzari, S., Bonina, D., Dubois, J.M., and Fournée, V., “Quasicrystal-Polymer Composites for Selective Laser Sintering Technology,” Materials and Design, 35, pp.691-695, (2012).CrossRefGoogle Scholar
Cao, Z., Ouyang, L., Wang, H., Liu, J.W., Sun, L.X., and Zhu, M., “Composition Design of Ti–Cr–Mn–Fe Alloys for Hybrid High-Pressure Metal Hydride Tanks,” Journal of Alloys and Compounds, 639, pp.452-457, (2015).CrossRefGoogle Scholar
Yang, L.Z., Gao, Y., Pan, E., and Waksmanski, N., “An Exact Solution for a Multilayered Two-Dimensional Decagonal Quasicrystal Plate,” International Journal of Solids and Structures, 51(9), pp.1737-1749, (2014).CrossRefGoogle Scholar
Ali, F., Scudino, S., Anwar, M.S., Shahid, R.N., Srivastava, V.C., Uhlenwinkel, V., Stoica, M., Vaughan, G., and Eckert, J., “Al-Based Metal Matrix Composites Reinforced with Al–Cu–Fe Quasicrystal-line Particles: Strengthening by Interfacial Reaction,” Journal of Alloys and Compounds, 607, pp.274-279, (2014).CrossRefGoogle Scholar
Li, Y., Yang, L.Z. and Gao, Y., “an Exact Solution for a Functionally Graded Multilayered One-Dimensional Orthorhombic Quasicrystal Plate,” Acta Mechanica, 230(4), pp.1257-1273, (2017).CrossRefGoogle Scholar
Li, Y., Yang, L.Z. and Gao, Y., “Thermo-Elastic Analysis of Functionally Graded Multilayered Two-Dimensional Decagonal Quasicrystal Plates,” Journal of Applied Mathematics and Mechanics, 98(9), pp.1585-1602, (2018).Google Scholar
Zhang, L., Guo, J. and Xing, Y., “Nonlocal Analytical Solution of Functionally Graded Multilayered One-Dimensional Hexagonal Piezoelectric Quasicrystal Nanoplates,” Acta Mechanica, 230(5), pp.1781-1810, (2019).CrossRefGoogle Scholar
Ding, D., Yang, W., Hu, C., and Wang, R.H., “Generalized Elasticity Theory of Quasicrystals,” Phys Rev B Condens Matter, 48(10), pp.7003-7010, (1993).CrossRefGoogle ScholarPubMed
Bak, P., “Phenomenological Theory of Icosahedral Incommensurate (“Quasiperiodic”) Order in Mn-Al Alloys,” Physical Review Letters, 54(14), pp. 5764-5772, (1985).CrossRefGoogle ScholarPubMed
Zhao, X.F. and Li, X., “the Scattering of SH Wave on Linear Crack in One-Dimensional Hexagonal Quasicrystal”, Chinese Journal of Computational Mechanics, 5, pp.693-698, (2015).Google Scholar
Liu, J.J and Shi, W.C., “D’Alembert Solution of Waves in a Bar of One-Dimensional Quasi-Crystals”, Journal of shanghai maritime university, 26(1), pp.77-80, (2005).Google Scholar
Sladek, J., Sladek, V. and Pan, E., “Bending Analyses of 1D Orthorhombic Quasicrystal Plates,” International Journal of Solids and Structures, 50(24), pp.3975-3983, (2013).CrossRefGoogle Scholar
Waksmanski, N., Pan, E., Yang, L.Z., and Gao, Y., “Free Vibration of a Multilayered One-Dimensional Quasi-crystal Plate,” Journal of Vibration and Acoustics, 136(4), pp.041019-1-8, (2014).CrossRefGoogle Scholar
Wang, X., “The General Solution of One-Dimensional Hexagonal Quasicrystal,” Mechanics Research Communications, 33(4), pp.576-580, (2006).CrossRefGoogle Scholar
Liu, Z.H., Xu, Y.Z. He, C.F., and Wu, B.G., “Experimental Study on Defect Imaging Based on Single Lamb Wave Mode in Plate-Like Structures,” Engineering Mechanics, 31(4), pp.232-238, (2014).Google Scholar
Wu, B., Xie, X.D., Li, Y.H., Liu, Z.H., He, C.F. and Xie, W.D., “Experiment Research on Propagation Characteristics of Low-Frequency Ultrasonic Longitudinal Guided Waves in Steel Floral Pipes,” Engineering Mechanics, 29(1), pp.319-324(2012).Google Scholar
Coccia, S., Bartoli, I., Marzani, A., Scalea, F.L., Salamone, S., and Fateh, M., “Numerical and Experimental Study of Guided Waves for Detection of Defects in the Railhead,” NDT and E International, 44(1), pp.93-100, (2011).Google Scholar
Zhang, X., “Non-Destructive Evaluation of Spiral-Welded Pipes Using Flexural Guided Waves,” 42ND ANNUAL REVIEW OF PROGRESS IN QUANTITATIVE NONDESTRUCTIVE EVALUATION: Incorporating the 6th European-American Workshop on Reliability of NDE, Minneapolis, American (July 26–31, 2015)Google Scholar
Lefebvre, J.E., Yu, J.G., Ratolojanahary, F.E., Elmaimouni, L., Xu, W. J., and Gryba, T., “Mapped Orthogonal Functions Method Applied to Acoustic Waves-Based Devices,” AIP Advances, 6, pp.065307, (2016).CrossRefGoogle Scholar
Wang, Y.W., Wu, T.H., Li, X.Y. and Kang, G.Z., “Fundamental Elastic Field in an Infinite Medium of Two-Dimensional Hexagonal Quasicrystal with a Planar Crack: 3D Exact Analysis,” International Journal of Solids and Structures, 66, pp.171-183, (2015).CrossRefGoogle Scholar
Han, X. and Liu, G.R., “Elastic Waves in a Functionally Graded Piezoelectric Cylinder,” Smart Materials and Structures, 12(6), pp.962-971, (2003).CrossRefGoogle Scholar
Chen, W.Q., Wang, H.M. and Bao, R.H., “on Calculating Dispersion Curves of Waves in a Functionally Graded Elastic Plate,” Composite Structures, 81(2), pp:233-242, (2007).CrossRefGoogle Scholar